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A sealed cylindrical vessel of height 10 cm and cross-sectional area 10 cm² is filled with water at 50 degC. The curved wall is adiabatic, but the two flat ends are 1 mm thick aluminium (K = 200 J/m-s-degC). The surroundings are at 20 degC. With density of water 1000 kg/m³ and specific heat 4200 J/kg-degC, estimate the time for the water temperature to drop by 1.0 degC (treat the heat current as constant over this small drop).

1. 0.035 s
2. 0.040 s
3. 0.045 s
4. 0.050 s

Correct answer: 0.035 s

Solution

Q = m c deltaT = (1000*1e-4*0.1)*4200*1 = 420 J; H = K*(2A)*(30)/(1e-3) = 200*2e-3*30/1e-3 = 1.2e4 W; t = 420/12000 = 0.035 s.

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